Related papers: Solution for a non linear Schr\"odinger equation v…
The two-dimensional cubic nonlinear Schrodinger equation (NLS) can be used as a model of phenomena in physical systems ranging from waves on deep water to pulses in optical fibers. In this paper, we establish that every one-dimensional…
The nonlinear Schr{\"o}odinger (NLS) equation, which incorporates higher-order dispersive terms, is widely employed in the theoretical analysis of various physical phenomena. In this study, we explore the non-commutative extension of the…
Non linear fiber optics concerns with the non linear optical phenomena occurring inside optical fibers. The propagation of light in single-mode fibers is governed by the one-dimensional nonlinear Schr\"odinger equation (NLS) in the presence…
The solution of the problem on reduction operators and nonclassical reductions of the Burgers equation is systematically treated and completed. A new proof of the theorem on the special "no-go" case of regular reduction operators is…
Recently, a new model of propagation of the light through the so-called weakly three-dimensional Cole-Cole nonlinear medium with short-range nonlocality has been proposed. In particular, it has been shown that in the geometrical optics…
In this paper we are extending the well known integrability theorems obtained by multiple scale techniques to the case of linearizable difference equations. As an example we apply the theory to the case of a differential-difference…
A nonlocal nonlinear Schr\"odinger (NLS) equation was recently found by the authors and shown to be an integrable infinite dimensional Hamiltonian equation. Unlike the classical (local) case, here the nonlinearly induced "potential" is $PT$…
We study the modulational stability of the nonlinear Schr\"odinger equation (NLS) using a time-dependent variational approach. Within this framework, we derive ordinary differential equations (ODEs) for the time evolution of the amplitude…
We show that a recently given nonautonomous nonlinear Schrodinger equation (NLSE) can be transformed into the autonomous NLSE.
We interpret the lens transformation (a variant of the pseudoconformal transformation) as a pseudoconformal compactification of spacetime, which converts the nonlinear Schr\"odinger equation (NLS) without potential with a nonlinear…
We present a noncommutative version of the Burgers equation which possesses the Lax representation and discuss the integrability in detail. We find a noncommutative version of the Cole-Hopf transformation and succeed in the linearization of…
The nonlinear Schr\"odinger (NLS) equation is a fundamental model for the nonlinear propagation of light pulses in optical fibers. We consider an integrable generalization of the NLS equation which was first derived by means of…
Some classes of the rational, periodic and solitary wave solutions for the Burgers hierarchy are presented. The solutions for this hierarchy are obtained by using the generalized Cole - Hopf transformation.
We explore a connection of the deterministically forced Burgers equation for local velocity fields with probabilistic solutions of the Schr\"{o}dinger boundary data problem. An issue of deducing the most likely interpolating dynamics from…
It is shown that using the similarity transformations, a set of three-dimensional p-q nonlinear Schrodinger (NLS) equations with inhomogeneous coefficients can be reduced to one-dimensional stationary NLS equation with constant or varying…
A two-dimensional generalized cubic nonlinear Schr\"odinger equation with complex coefficients for the group dispersion and nonlinear terms is used to investigate the evolution of a finite-amplitude localized initial perturbation. It is…
We present an introduction to the nonlinear Schr\"odinger equation (NLSE) with concentrated nonlinearities in $\mathbb{R}^2$. Precisely, taking a cue from the linear problem, we sketch the main challenges and the typical difficulties that…
The method of solving of nonlinear Schr\"odinger equation is considered. Some examples of its applications are demonstrated.
For the problem of Burgers turbulence with random gaussian forcing a similarity functional solution of Hopf equation is presented and compared with scaling arguments and replica Bethe-anzatz treatments. The corresponding field theory is…
We consider vector Non-linear Schrodinger Equation(NLSE) with balanced loss-gain(BLG), linear coupling(LC) and a general form of cubic nonlinearity. We use a non-unitary transformation to show that the system can be exactly mapped to the…